CFA CFA Level 1 Computing Implied Forward Rates

# Computing Implied Forward Rates

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Question-(1+0.02062/2)To the power of 4*(1+3f2/2)To the power of 6=(1+0.02243/2)To the power of 10

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This is the full question:

(1+zA)A x (1+IFRA,B-A)B-A – (1+zB)B

Suppose that the yields-to-maturity on a 3-year and 4-year zero coupon bonds are 3.5% and 4% on a semi-annual basis. The “3y1y” implies that the forward rate could be calculated as follows:

A = 6 periods

B = 8 periods

B-A = 2 periods

z6 = 0.035/2 = 0.0175

z8 = 0.04/2 = 0.02

(1+0.0175)6 x (1+IFR6,2)2 = (1+0.02)8

IFR6,2 = 0.0275

The “3y1y” implies the forward rate or forward yield is 5.50% (0.0275% x 2)

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Can’t understand the notation well enough – in any case wouldn’t the answer show the calculations?

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This one doesn’t seem right. Replacing IFR6,2 with 0.0275 in the LHS equation doesn’t yield the RHS.

Edit: You posted the wrong notation, it’s (1+0.0175)^6 x (1+IFR6,2)^2 = (1+0.02)^8

(1+0.0175)^6 x (1+IFR6,2)^2 = (1+0.02)^8

1.0175^6 x (1+IFR6,2)^2 = 1.02^8

1.1097 x (1+IFR6,2)^2 = 1.1717

(1+IFR6,2)^2 = 1.1717 / 1.1097

(1+IFR6,2)^2 = 1.0558

1+IFR6,2 = 1.0558^(1/2)

1+IFR6,2 = 1.0275

IFR6,2 = 0.0275

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What? Your original question and follow-ups seems totally different, even the answers.

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Yea its just a different question but would use the same concept to get to the answer….I just thought i send you a full version of a question i found online. please note the 6, 2 and 8 after the bracket in the equation is to the power of 6, 2 and 8

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any input on this one Min?

its mainly here I’m getting lost with the algebra:

(1+0.0175)6 x (1+IFR6,2)2 = (1+0.02)8

IFR6,2 = 0.0275

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Maybe this is easier to see, how do they get to that answer, this is all that is given

(1+0.0175)6 x (1+IFR6,2)2 = (1+0.02)8

IFR6,2 = 0.0275